Question

The function f(x) = 1500x^2+90,000 models a company's annual earnings over the past several

years, where x represents the number of years the company has been in business.
Formulate and solve an equation that can be used to determine when the company should expect to reach
$240,000 in annual earnings if the function continues to be a valid model.

Answer 1

x = 10 years

Explanation:

Since f(x) represents the annual earnings and we want to know the time in years when the company's earnings should reach this, we can use the equation 240000 = 1500x^2 + 90000 to solve for x:

`240000=1500x^2+90000\\150000=1500x^2\\100=x^2\\10=x\\-10=x`

Square roots require you to have two solutions (one negative and one positive), but since you can't have negative years, the answer is simply 10 years.